4.2. Analysis of Concrete Tensile Damage
Characteristics
To systematically reveal the evolutionary mechanisms of
concrete axial tensile damage, the following analysis employs
a combined approach integrating time-history analysis and
cluster analysis to investigate the AE signals.
4.2.1. DAMAGE STAGE DIVISION BASED ON TIME HISTORY
ANALYSIS
The cumulative impact count of acoustic emissions can
provide an overall reflection of the intensity of acoustic emis-
sions and is often utilized to describe the accumulation of
damage within materials. Therefore, it can be employed to
depict the damage progression of concrete. Since the failure
times of concrete specimens C1, C2, and C3 under tensile
loading vary, time is normalized to more clearly discern the
damage characteristics of different specimens. Additionally, the
test is uniformly loaded, with time corresponding one-to-one
with the stress level.
As shown in Figure 8, the time-series curves of cumula-
tive impact counts of acoustic emissions during the concrete
tensile failure process exhibit similar patterns of change. They
all approximately follow an increasing trend, with a tendency
to rise in a parabolic manner. Based on the different curva-
tures of the parabolas, the cumulative impact count curves of
concrete acoustic emissions can be divided into three stages.
Stage D1 (0–20% stress level) mainly corresponds to the
cracking of concrete. The growth trend of the AE hit count is
relatively slow, indicating low AE activity. In this stage, many
new microcracks are initiated in the concrete under tensile
stress, leading to a continuous generation of AE signals. As a
result, the cumulative hit count shows a slow growth trend.
In stage D2 (20–75% stress level), concrete undergoes
further cracking as the concrete matrix material gradually
bears the load. Particularly after reaching peak stress, the
number of microcracks continues to increase over a consider-
able period, with new cracks gradually developing and even-
tually merging with existing cracks and pores in the concrete.
This leads to more noticeable AE activity, causing the trend of
the cumulative hit count to accelerate.
In stage D3 (75–100% stress level), the cracking of the
concrete matrix has reached a certain width, and cracks are
stably expanding, eventually forming macroscopic cracks. This
is the stage where concrete undergoes axial tensile damage
and failure, characterized by the rapid propagation of cracks.
Consequently, fluctuations in the AE cumulative hit count
become more pronounced during this stage.
4.2.2. CLASSIFICATION OF DAMAGE DEGREE BASED ON
CLUSTER ANALYSIS
From Figure 7, it can be seen that the AE signals of concrete
under axial tensile damage exhibit three-cluster characteristics
in the clustering results. The numerical values of the centers
for the three clusters are shown in Table 5.
From Table 5, we can see that the first cluster of AE signals
has low intensity and high frequency, representing mild
damage in concrete under axial tensile stress. This mainly
involves the initiation of microcracks in the concrete, consis-
tent with the damage mechanism of stage D1 identified in the
ME
|
AXIALTENSION
0
1000 D1
D2
D3
2000
3000
4000
5000
6000
0 0.2 0.4 0.6 0.8 1.00
Time (normalized)
Category 1
Category 2
Category 3
4
0
0 2 0 0 0 8
y
ategory
Figure 8. Normalized time history curve of AE cumulative impact
number during axial tensile process of concrete.
6000
700
8000
900
4000
500
200
300
100
0 50 100
Ring count
150 200 2502
0
0
1
1 2
Figure 7. AE optimal clustering results of concrete axial tensile damage.
TA B L E 5
Cluster center of ring count–center frequency
Clustering results Ring count Center frequency (kHz) Signal proportion (%)Damage stage
Category 1 2.3676 595.7006 25 Mild
Category 2 7.0207 499.5985 30 Medium
Category 3 37.0240 341.0939 45 Severe
48
M AT E R I A L S E V A L U AT I O N • M AY 2 0 2 5
Accumulated
number
of AE
impacts
C
frequency y

time history analysis. The second cluster has moderate inten-
sity and moderate frequency, indicating moderate damage,
with the primary phenomenon being the expansion of micro-
cracks in the concrete, matching the damage mechanism of
stage D2. The third cluster has low intensity and low frequency,
indicating severe damage, mainly due to the formation of mac-
roscopic cracks in the concrete, which aligns with the damage
mechanism of stage D3. The cumulative hit count time history
curves for the three clusters are plotted in Figure 9, provid-
ing further validation for the classification of damage levels in
concrete.
From Figure 9, it is evident that the cumulative hit count
time history curves for the three clustered results of concrete
acoustic emissions exhibit noticeable differences across the dif-
ferent damage stages. In stage D1, the AE activity represented
by the three time history curves tends to be consistent, indi-
cating a quiet period. In stage D2, the second and third types
of signals begin to show significant growth as the stress level
increases, with signals of moderate and severe damage over-
taking those of mild damage, gradually becoming dominant. In
stage D3, the AE activity of the third type of signal, representing
severe damage, increases significantly, becoming the dominant
signal in this stage.
In summary, the distribution of time history curves for the
three types of signals representing concrete damage levels after
clustering analysis shows dominance in their corresponding
damage stages. This further corroborates that the clustering
analysis results align with the AE characteristics of the three
damage stages described earlier.
4.2.3. JOINT ANALYSIS OF DAMAGE MECHANISMS
To further explore the comprehensive information on concrete
damage mechanisms hidden behind the optimal clustering
results, the study calculates the average values of AE feature
parameters corresponding to each cluster of the ring count–
center frequency combination, as summarized in Table 6.
From Table 6, it can be seen that the average values of the
AE feature parameters for the three types of AE signals have
noticeable numerical differences, confirming that the optimal
clustering combination chosen in this study effectively classi-
fies concrete axial tensile damage information. By examining
the differences in the average values of AE feature parameters,
this study explores the concrete damage mechanism informa-
tion underlying the three levels of damage severity.
In the first type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which repre-
sent signal intensity, are at relatively low levels. At the same
time, the rise time and duration, which represent the signal’s
duration, are at relatively high levels. This indicates that this
type of signal is characterized by low signal intensity and long
duration, typical of the quiet period in concrete axial tensile
damage. During this stage, the primary processes are the
expansion of existing cracks and the initiation of microcracks
in the concrete material. This can be identified as the signal
for the initiation of microcracks in concrete, consistent with
the characteristics of mild damage derived from the clustering
center analysis earlier.
In the second type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which represent
signal intensity, are at moderate levels. Additionally, the rise
time and duration, which indicate the signal’s duration, are also
at moderate levels. This suggests that this type of signal is char-
acterized by moderate signal intensity and duration. Thus, this
signal can be identified as representing the expansion of micro-
cracks in concrete, aligning with the characteristics of moderate
damage derived from the clustering center analysis earlier.
In the third type of AE signal in concrete, the ring count,
energy, signal strength, and absolute energy, which represent
signal intensity, are at relatively high levels. Meanwhile, the rise
time and duration, which indicate the signal’s duration, are
at relatively low levels. This suggests that this type of signal is
characterized by high signal intensity but a rapid rate of signal
decay, typical of strong excitation signals. Thus, this signal
can be identified as representing the cracking of macroscopic
cracks in concrete, consistent with the characteristics of severe
damage derived from the clustering center analysis earlier.
0
10001
5005
15001
D11
D2
D33 2000
2500
0 0.2 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time (normalized)
Category 1
Category 2
Category 3
0
0 2 0 0 3 0 4 0 5 0 6 0 0 8 0 9 0
y
ategory
Figure 9. Normalized time history curve of cumulative impact number
of three types of concrete AE signals.
TA B L E 6
The average values of AE characteristic parameters of concrete optimal cluster center
Clustering results Rise time (µs) Ring count Energy (pV-s) Duration (µs) Signal strength (pV-s) Absolute energy (aJ)
Category 1 36.14 2.36 0.06 473.35 2565.92 3.65
Category 2 14.51 7.02 0.32 65.58 1983.42 15.79
Category 3 8.81 37.02 6.34 39.79 42759.19 6404.17
M AY 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 49
Accumulated
number
of AE
impacts